Various data processing systems have been developed including storage systems, cellular telephone systems, and radio transmission systems. In such systems data is transferred from a sender to a receiver via some medium. For example, in a storage system, data is sent from a sender (i.e., a write function) to a receiver (i.e., a read function) via a storage medium. As information is stored and transmitted in the form of digital data, errors are introduced that, if not corrected, can corrupt the data and render the information unusable. Data processing typically relies on transferring an encoded data set via a medium, and decoding the received encoded data set to recover the original data. In some cases, the encoding and decoding results in a mis-correction situation where the original data is not recovered, but the decoding is not correct.
Hence, for at least the aforementioned reasons, there exists a need in the art for advanced systems and methods for data encoding and/or decoding.